The invention is related to a feedback-control method for an asymmetric differential pressure transducer.
The invention also concerns an apparatus for the feedback-control of an asymmetric differential pressure transducer.
A micromechanical element kept at a given electric potential can be controlled by an electrostatic force which is generated by means of potential differences applied to the electrodes surrounding the element and the element itself. As known, the electrostatic force generated between two electrodes is expressed as: ##EQU1## where U is the potential difference between planar electrodes, .epsilon..sub.r, dielectric coefficient of the medium, dA elementary area element and d distance between the planar electrodes. The integration is carried out over the electrode surface. On the basis of Eq. (1), the electrostatic force between the electrodes can be interpreted as an electrostatic pressure acting on the electrode surface: ##EQU2##
Next, a differential pressure transducer structure is examined comprising a body structure supporting a fixed electrode and a diaphragm attached at its edges to said body structure and adapted to deflect under an imposed differential pressure. If the deflection of the diaphragm remains extremely small, each surface element of the diaphragm will be subjected to an equally large force effect by both the electrostatic pressure expressed by Eq. (2) and the externally applied physical pressure, which is thus cancelled by the electrostatic pressure at any point of the diaphragm surface, that is, p.sub.ext =p.sub.electric. This means that a differential pressure transducer can be operated as a servotransducer in an electrically feedback-connected mode. When the diaphragm is controlled to the nondeflected state, the external pressure can be expressed as: ##EQU3## where Q is the charge on the electrodes.
Such a feedback arrangement is, however, handicapped by three basic problems:
1) The relationship between the electrostatic pressure and the feedback control voltage employed as the transducer output voltage is nonlinear on the basis of Eq. (2). PA1 2) The equation p.sub.ext =.epsilon..sub.0 .epsilon..sub.r U.sup.2 /2d.sup.2 is valid in a force balance state only when the diaphragm deflection is zero. To identify this state, the diaphragm position must be known. PA1 3) The factor linking the feedback voltage to the generated electrostatic pressure is dependent on the dielectric coefficient of the medium between the electrodes.
A solution to these problems is disclosed in U.S. Pat. No. 5,095,750 to Suzuki et al., "Semiconductor Capacitance-Type Accelerometer with PWM Electrostatic Servo Technique", by S. Suzuki, S. Tuchitani, K. Sato, S. Ueno, Y Yokota, M. Sato and M. Esashi, Sensors and Actuators A21-A23, pp. 316-319, 1990 and Design and Test of a Precision Servoaccelerometer with Digital Output, by Y. de Coulon, T. Smith, J. Herman, M. Chevroulet and F. Rudolf, The Proceedings of the 7th International Conference on Solid-State Sensors and Actuators, Yokohama, Japan 1993, pp. 832-835. If the feedback arrangement is implemented using a pulse-width or pulse-rate modulated signal, i.e., with a constant-amplitude pulse (voltage level), a linear relationship can be established between the electrostatic pressure and the duty cycle of the pulse train: ##EQU4## where D=T.sub.ON /T.sub.total, that is, the ratio of the pulse ON time to the total pulse period. Eq. (4) may be further written as: ##EQU5## where U.sub.pulse is the amplitude of the pulse train, T.sub.pulse is the pulse width and f.sub.pulse =n/T.sub.total is the pulse rate (pulses/unit time). In conjunction with pulse-width modulation, a linear output voltage is obtained by taking the pulse train output signal via an integrator. A pulse-rate modulated signal can be directly processed as a digital signal formed by a bit stream. A problem of the pulsed feedback-control scheme is that the pulse train signal fed back as the control signal acts as an AC signal that may affect the capacitance measurement and even saturate the measurement circuits employed in the capacitance measurement.
A starting point for the design of a pulsed feedback control of an acceleration transducer is to operate appreciably above the transducer natural frequency (see U.S. Pat. 5,095,750 and the two articles referred to above) whereby the transducer seismic mass by its moment of inertia is not capable of exhibiting a fast response to individual pulses, and thus, the pulsed feedback force effect is averaged. By contrast, in a differential pressure transducer the diaphragm natural frequency is significantly higher (typically in the order of 30-200 kHz depending on the diaphragm thickness and diameter). However, when operated at atmospheric pressure, the diaphragm is subjected to extremely heavy viscose damping, so again the diaphragm is prevented from responding to individual pulses imposed at a high pulse rate, and also here the pulsed feedback force effect is averaged.
In capacitive measurement techniques, particularly when employing the force balance principle, a problem arises from the dependence of the dielectric coefficient on the temperature, humidity and other factors affecting the dielectric fill medium of the transducer. Therefore, the dielectric coefficient must be measured and its changes compensated for. Such a method is disclosed in U.S. Pat. No. 4,831,492 to Kusima according to which the actual transducing electrode of a pressure transducer is surrounded by another electrode having a low sensitivity to pressure change thus being suited for detecting changes in the dielectric coefficient.